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In "Points, Schmoints," Marty Bergen related an instance in which he announced "skip bid," before "jumping" his partner's two diamond bid to the five level (instead of three). According to him, his Left Hand Opponent had to wait ten seconds before reacting (in order not to give away information by the speed or slowness of his reaction to the unusual bid).

Are there many instances where tournament rules mandate that players take such a "time out" in either bidding or play?

OK, there is a "stop card" mechanism. But "more honored in the breach than the observance."
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Tom AuFeb 24 '13 at 20:07

More and more honoured in the observance than the breach, as you progress up the levels of expertise. The world of expert Bridge is a very small one, and at high levels respect for rule observance is significant.
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Pieter GeerkensJun 9 '13 at 19:39

Calls and plays should be made without undue emphasis, mannerism or inflection, and without undue hesitation or haste. But the Regulating Authority may require mandatory pauses, as on the first round of the auction, or after a skip-bid warning or on the first trick.

The ACBL is a Regulating Authority that does require mandatory pauses for skip bids. The ACBL Codified Minutes, Chapter XII, Section A have this to say:

A. How and When Made

Players should protect their rights and the opponent's by announcing, prior to making an opening bid on the two level or higher, or prior to making any subsequent bid that skips one or more levels of bidding:

When bidding orally by saying, "I am about to make a skip bid. Please Wait!"

When using bidding boxes, by placing the stop card so the LHO sees it (the skip bidder is responsible for gaining LHO's attention). The skip bid is made. The stop card is replaced in the bidding box.

...

C. Opponents of Skip Bidder

All Players

When RHO has announced a skip bid, the player following the skip bidder must wait for a suitable interval (about 10 seconds). In waiting the player's manner must be one that suggests he is an active participant in the auction (the hand should be studied during pause). any (sic) obvious display of disinterest is most improper.

I've never seen a director called to protest that opponents are not using the stop card but would expect to see one called if an opponent was clearly using the stop card only for weak bids. I have seen director calls after a player took far longer than 10 seconds to make a call after a skip bid and his partner took a bid at his next turn.

There is one additional "mandated time-out" in addition to the STOP card: When dummy comes down, declarer is required to study the hand for a few seconds before calling a card.

Depending on how closely dummy resembles any bidding made, that would be on the order of 3 to 5 seconds. To call a card quicker than this is highly unethical, and declarer's RHO is allowed to allowed to take this time in lieu if declarer refuses to do so. There is no inference penalty for opening leader in this case, as declarer has willfully instigated the situation.